Nonequilibrium theory for gain in quantum cascade lasers

A nonequilibrium theory for gain in quantum cascade lasers is presented. Optical absorption α at a given photon energy is calculated from the imaginary part of the optical susceptibility. The occupation functions for each electronic subband are calculated from the diagonal terms in the carrier Green´s functions (which are expanded in terms of Wannier-Stark states), and obtained by self-consistent solutions of Dyson equations. Scattering with phonons and impurities are included in the relevant self-energies. The resulting integral equation and gain spectra is shown.